Many conventional technologies for fabricating tissue engineering scaffolds are not suitable for fabricating scaffolds with patient-specific attributes. For example, many conventional technologies for fabricating tissue engineering scaffolds do not provide control over overall scaffold geometry or over cell position within the scaffold. In this study, the use of computer-aided laser micromachining to create scaffolds for vascular tissue networks was investigated. Computer-aided laser micromachining was used to construct patterned surfaces in agarose or in silicon, which were used for differential adherence and growth of cells into vascular tissue networks. Concentric three-ring structures were fabricated on agarose hydrogel substrates, in which the inner ring contained human aortic endothelial cells, the middle ring contained HA587 human elastin and the outer ring contained human aortic vascular smooth muscle cells. Basement membrane matrix containing vascular endothelial growth factor and heparin was to promote proliferation of human aortic endothelial cells within the vascular tissue networks. Computer-aided laser micromachining provides a unique approach to fabricate small-diameter blood vessels for bypass surgery as well as other artificial tissues with complex geometries.